Method and system for neighbor tier determination

ABSTRACT

A process for determining neighbor tier relationships between cells in a wireless telecommunications network includes establishing a plurality of cell points, each cell point representing a cell of a plurality of cells in the wireless telecommunications network, forming a plurality of triangles, the vertices of each triangle of the plurality of triangles corresponding to respective cell points of the plurality of cell points, removing edges from a portion of the plurality of triangles, determining neighbor tier relationships between the plurality of cells using remaining triangle edges between the plurality of cell points, storing the neighbor tier relationships in a first memory, and using the neighbor tier relationships for handovers between the plurality of cells.

CROSS-REFERENCES TO RELATED APPLICATIONS

The present invention claims priority to U.S. Provisional ApplicationNo. 62/108,482, filed Jan. 27, 2015, and to P.C.T. Application No.PCT/US15/52482, filed Sep. 25, 2015, which in turn claims priority toU.S. Provisional Application No. 62/055,580, filed Sep. 25, 2014, andU.S. Provisional Application No. 62/055,583, filed Sep. 25, 2014, eachof which are incorporated by reference herein for all purposes.

BACKGROUND

In order to serve the increased demand, wireless communication networksare becoming more diverse and complex, and subsequently are becomingmore difficult to manage. A Self-Organizing Network (SON) simplifies andautomates multiple processes to efficiently manage diverse communicationnetworks.

Many SON algorithms require information about the coverage areas ofcells in order to make better optimization decisions. However, it can bedifficult to obtain cell coverage information for a network. Cellcoverage information could be retrieved from the output of a networkplanning tool, but this information is not always available to a SONtool. In addition, network planning tools tend to use large amounts ofdata to determine cell coverage, so planning tools tend to be relativelyslow and inefficient.

Typical algorithms attempt to estimate the coverage area of a sourcecell by identifying the closest cells in the network to the source celland using information on the azimuth of the source cells to estimate acoverage distance for that cell. While these methods can produceacceptable results in networks where cells are laid out in a regularfashion, they tend to perform poorly in areas with an irregularplacement of cells.

In addition, some algorithms have absolute distance thresholds in placeto prevent against poor algorithmic decisions. For example, an AutomatedNeighbor Relations (ANR) algorithm may impose a maximum distancethreshold beyond which cells are not added to neighbor lists. Oneproblem with imposing such a threshold is that a single threshold isgenerally not suitable in all cases, especially when cell densityvaries.

For example, in rural environments, a large distance threshold such as15 km may be suitable. However, if this threshold is used in an urbanenvironment, distant cells may be added to the neighbor list of a sourcecell, resulting in poor system performance. In an urban environment, adistance threshold of 2 km to 4 km may be more suitable. However, if thedistance threshold is set too low, neighbor cells may not be added, eventhough manual inspection shows that they should be.

Distance thresholds are generally applied to a large number of cells ina region such as all cells on a particular Radio Network Controller(RNC). While different distance thresholds may be applied on a per-cellbasis, this is time consuming and error prone if done manually.

In practice, optimization engineers don't consider distances—instead,they look at cell tiers. Most RF engineers look at map and intuitivelyknow how many tiers separate cells. However, it can be hard for anoptimization engineer to provide a precise definition for a cell tier,or how to establish such a tier.

Most engineers will look at a map and make intuitive estimates aboutwhich cells are first tier neighbors of a source cell. Generally, thesewill be the closest cells to the source cells, with antenna pointingdirections that are pointing towards the coverage area of the sourcecell. However, these intuitive decisions are difficult to translate intoalgorithms. Therefore, it is desirable to have an accurate and efficienttool that automates the tier counting process.

BRIEF SUMMARY

Embodiments of this disclosure provide a method and a system forautomatically determining tier relationships between cells in a wirelesstelecommunications network. When Delaunay triangulation is used todetermine neighbor relations, an initial triangulation can be improvedby using distance and/or angle-based criteria for removing long edges oftriangles, which in a conventional network would normally not beconsidered to be first tier neighbors. Modified first-tier assignmentsare used to improve the tier counts between cells in a cellular network.These in turn may be used to update the neighbor lists for each cell,which can then be used by mobile terminals for handover purposes.

In an embodiment, a process for determining neighbor tier relationshipsbetween cells in a wireless telecommunications network includesestablishing a plurality of cell points, each cell point representing acell of a plurality of cells in the wireless telecommunications network,forming a plurality of triangles, the vertices of each triangle of theplurality of triangles corresponding to respective cell points of theplurality of cell points, removing edges from a portion of the pluralityof triangles, determining neighbor tier relationships between theplurality of cells using remaining triangle edges between the pluralityof cell points, storing the neighbor tier relationships in a firstmemory, and using the neighbor tier relationships for handovers betweenthe plurality of cells. Forming a plurality of triangles may includeperforming Delaunay triangulation on the plurality of cell points.

A process may include applying a length-based or angle-based criterionto identify triangle edges for removal, wherein the triangle edgesidentified for removal are longest edges of respective triangles.Removing edges from a portion of the plurality of triangles may includecomparing lengths of triangle edges to a predetermined value, andtriangle edges whose lengths exceed the predetermined value are theedges of the portion of the plurality of triangles that are removed.

In an embodiment, removing edges from a portion of the plurality oftriangles includes determining a middle angle value of angles for eachtriangle and comparing the middle angle value to a predetermined value,wherein longest edges of the triangles whose middle angle values areless than the threshold value are the edges of the portion of theplurality of triangles that are removed.

In an embodiment, removing edges from a portion of the plurality oftriangles includes determining a minimum angle value of angles for eachtriangle and comparing the minimum angle value to a predetermined value,wherein longest edges of the triangles whose minimum angles are lessthan the threshold value are the edges of the portion of the pluralityof triangles that are removed.

In an embodiment, removing edges from a portion of the plurality oftriangles includes determining lengths of the longest edges of thetriangles, determining minimum angles of the triangles, determiningratios between respective longest edge lengths and respective minimumangles for each triangle, and comparing the ratios to a predeterminedvalue, wherein longest edges of the triangles whose ratios are less thanthe threshold value are the edges of the portion of the plurality oftriangles that are removed.

In an embodiment, a plurality of triangle edges are identified ascandidates for removal before removing the edges, and trianglesassociated with the candidate edges are stored in a second memory. In anembodiment, the first memory and the second memory may be differentlocations in the same apparatus such as a network resource controller.In another embodiment, the first memory may be a first network equipmentsuch as a base station, and the second memory may be in a second networkequipment such as a SON controller.

In an embodiment, the method further comprises determining whether anedge of a first triangle that is a candidate for removal is shared witha second triangle, when the edge of the first triangle is shared withthe second triangle, determining whether the second triangle has an edgethat has been removed or is a candidate for removal and when the secondtriangle does not have an edge that has been removed or is a candidatefor removal, retaining the shared edge.

In an embodiment, the method further comprises determining whether anedge of a first triangle that is a candidate for removal is shared witha second triangle, when the edge of the first triangle is shared withthe second triangle, determining whether the second triangle has an edgethat has been removed or is a candidate for removal, and when the secondtriangle has an edge that has been removed or is a candidate forremoval, removing the shared edge from the first and second triangles.When the edge of the first triangle is not shared with the secondtriangle, the edge may be removed.

In an embodiment of this disclosure, a computer-implemented method fordetermining a neighbor tier relationship between first and second cellsin a wireless communications network that includes a plurality of cellsites includes establishing respective cell site shapes for theplurality of cell sites including the first and second cells, each shaperepresenting a coverage area of a corresponding cell site, establishingcell shapes for the cells of the plurality of cell sites, determining atier relationship between the first and second cells based on a numberof cell polygons between the first and second cells, and storing thetier relationship in a memory.

In an embodiment, establishing cell shapes for the cells of theplurality of cell sites includes determining cell points for cells ofthe plurality of cell sites and creating a second Voronoi diagram usingthe cell points as seeds. Establishing respective cell site shapes forthe plurality of cell sites may include determining locations for eachof the plurality of cell sites and creating a first Voronoi diagramusing the cell site locations as seeds.

The method may further include determining cell points for cells of theplurality of cell sites. In such an embodiment, determining cell pointsfor cells of the plurality of cell sites may include determining adistance from a first cell site of the plurality of cell sites to anearest neighboring cell site and establishing cell points for the firstcell site at locations that are a fraction of the distance from thefirst cell site. The fraction of the distance may be a value from 0.05to 0.50, and the cell points may be established at azimuth directionsfor antennas of the first cell site. Furthermore, the nearestneighboring cell site may be determined by performing Delaunaytriangulation on the plurality of cell sites,

In an embodiment, the method may further include performing Delaunaytriangulation on the cell points. Such an embodiment may further includedetermining first tier relationships between cells associated with thecell points by identifying cells that are connected by a single leg oftriangles from the Delaunay triangulation as first tier neighbors. Inaddition, determining first tier relationships may be performed for allcells of the plurality of cell sites, and it may further includecounting a number of first tier relationships between the first cell andthe second cell, wherein the number of first tier relationships is thetier relationship between the first cell and the second cell.

In an embodiment, determining the tier relationship between the firstand second cells includes determining a least number of triangle legs ofthe Delaunay triangles that connect the first cell to the second cell.The cell shapes and/or the cell site shapes may be Voronoi polygons. Inan embodiment, the tier relationship between the first cell and thesecond cell is determined based on a lowest number of Voronoi polygonsbetween the first and second cells.

Tier counting may include determining a lowest number of polygon edgesthat must be traversed between the first cell and the second cell,wherein the lowest number of polygon edges is a value of the tierrelationship between the first and second cells.

In an embodiment, tier counting includes establishing a line between oneof first or second cell points corresponding to the first and secondcells or first or second cell sites corresponding to the first andsecond cells and determining a number of cell shapes that intersect withthe line, wherein the number of cell shapes that intersect with the lineis a value of the tier relationship between the first and second cells.

When a cell site uses an omnidirectional antenna, the cell point may bethe location of the cell site. A method may further include updating aneighbor list based on the tier relationship.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a wireless communications system according to anembodiment.

FIG. 2 illustrates a network resource controller according to anembodiment

FIG. 3 illustrates an automatic tier counting process according to anembodiment.

FIG. 4 illustrates a process for establishing a shape around a cellsite.

FIG. 5A illustrates site locations as shapes in a regular deployment.

FIG. 5B illustrates site locations as shapes in a variable densitydeployment.

FIG. 6 illustrates a process for determining tier relationships betweencells.

FIGS. 7A, 7B and 7C illustrate determining tier relationships betweencells.

FIG. 8A is a Voronoi diagram of cell sites, and FIG. 8B is a Voronoidiagram of cell points.

FIG. 9 illustrates a process for determining tier relationships betweencells.

FIGS. 10A and 10B illustrate determining tier relationships betweencells.

FIGS. 11A and 11B illustrate determining shapes based on cell type.

FIG. 12 illustrates a process for determining tier relationships betweencells.

FIGS. 13A and 13B illustrate determining tier relationships betweencells.

FIG. 14 illustrates a process for determining tier relationships betweencells.

FIG. 15 illustrates tier relationships between cells.

FIG. 16 illustrates a process for determining tier relationships betweencells.

FIG. 17 illustrates tier relationships between cells.

FIG. 18 illustrates a process for determining tier relationships betweencells.

FIG. 19 illustrates a process for determining tier relationships betweencells.

FIG. 20 illustrates determining tier relationships between cells.

FIG. 21 illustrates a process for determining neighbor relationshipsaccording to an embodiment of the present disclosure.

FIG. 22 illustrates a plurality of cell points connected by Delaunaytriangulation.

FIG. 23 illustrates a plurality of cell points connected by Delaunaytriangulation in which selected edges are designated for removal.

FIG. 24 illustrates a plurality of cell points connected by Delaunaytriangulation from which selected edges have been removed.

FIG. 25 illustrates a distance-based process for selecting edges forremoval.

FIG. 26 illustrates a plurality of cell points connected by Delaunaytriangulation in which selected edges are designated for removal using adistance-based method.

FIG. 27 illustrates an angle-based process for selecting edges forremoval.

FIG. 28 illustrates an asymmetrical triangle.

FIG. 29 illustrates a plurality of cell points connected by Delaunaytriangulation in which selected edges are designated for removal usingan angle-based method.

FIG. 30 illustrates an angle-based process for selecting edges forremoval.

FIG. 31 illustrates an angle-based process for selecting edges forremoval.

FIG. 32 illustrates a process for removing edges.

FIG. 33 illustrates a plurality of cell points connected by Delaunaytriangulation in which selected edges are designated for removal.

DETAILED DESCRIPTION

In the following description, neighbor tiers are related to coveragearea boundaries. In particular, two neighboring cells are first tierneighbors when their respective coverage areas share a common cellboundary. In addition, second tier neighbors have coverage areas thatare separated by one other cell, while third tier neighbors havecoverage areas that are separated by two other cells, and so on. Thisexplanation is consistent with expectations from RF engineers for tierrelationships.

This disclosure provides a method and system for determining the numberof tiers separating cells in a cellular communications network. Thisinformation can then be used in algorithms for self-organizing networks,such as Automatic Neighbor Relations (ANR), Neighbor ListInitialization, Coverage and Capacity Optimization (CCO), Reuse CodeOptimization (e.g., Scrambling Code Optimization for UMTS networks, PCIOptimization for LTE Networks, BSIC optimization for GSM networks,etc.). Various cellular parameters may be changed in conjunction withthese activities, such as transmit power and antenna tilt and direction.

A detailed description of embodiments is provided below along withaccompanying figures. The scope of this disclosure is limited only bythe claims and encompasses numerous alternatives, modifications andequivalents. Although steps of various processes are presented in aparticular order, embodiments are not necessarily limited to beingperformed in the listed order. In some embodiments, certain operationsmay be performed simultaneously, in an order other than the describedorder, or not performed at all.

Numerous specific details are set forth in the following description inorder to provide a thorough understanding. These details are providedfor the purpose of example and embodiments may be practiced according tothe claims without some or all of these specific details. For thepurpose of clarity, technical material that is known in the technicalfields related to this disclosure has not been described in detail sothat the disclosure is not unnecessarily obscured.

FIG. 1 illustrates a networked communications system 100 according to anembodiment of this disclosure. System 100 may include one or more basestations 102, each of which are equipped with one or more antennas 104.Each of the antennas 104 may provide wireless communication for userequipment 108 in one or more cells 106. As used herein, the term “basestation” refers to a wireless communications station provided in alocation and serves as a hub of a wireless network. For example, in LTE,a base station may be an eNodeB. The base stations may provide servicefor macrocells, microcells, picocells, or femtocells. In thisdisclosure, the term “cell site” may be used to refer to the location ofa base station.

The one or more UE 108 may include cell phone devices, laptop computers,handheld gaming units, electronic book devices and tablet PCs, and anyother type of common portable wireless computing device that may beprovided with wireless communications service by a base station 102. Inan embodiment, any of the UE 108 may be associated with any combinationof common mobile computing devices (e.g., laptop computers, tabletcomputers, cellular phones, handheld gaming units, electronic bookdevices, personal music players, MiFi™ devices, video recorders, etc.),having wireless communications capabilities employing any commonwireless data communications technology, including, but not limited to:GSM, UMTS, 3GPP LTE, LTE Advanced, WiMAX, etc.

The system 100 may include a backhaul portion 116 that can facilitatedistributed network communications between backhaul equipment 110, 112and 114 and the one or more base station 102. As would be understood bythose skilled in the Art, in most digital communications networks, thebackhaul portion of the network may include intermediate links 118between a backbone of the network which are generally wire line, and subnetworks or base stations located at the periphery of the network. Forexample, cellular user equipment (e.g., UE 108) communicating with oneor more base station 102 may constitute a local sub network. The networkconnection between any of the base stations 102 and the rest of theworld may initiate with a link to the backhaul portion of a provider'scommunications network (e.g., via a point of presence).

In an embodiment, the backhaul portion 102 of the system 100 of FIG. 1may employ any of the following common communications technologies:optical fiber, coaxial cable, twisted pair cable, Ethernet cable, andpower-line cable, along with any other wireless communication technologyknown in the art. In context with various embodiments of the invention,it should be understood that wireless communications coverage associatedwith various data communication technologies (e.g., base station 102)typically vary between different service provider networks based on thetype of network and the system infrastructure deployed within aparticular region of a network (e.g., differences between GSM, UMTS,LTE, LTE Advanced, and WiMAX based networks and the technologiesdeployed in each network type).

Any of the network controller devices 110, 112 and 114 may be adedicated Network Resource Controller (NRC) that is provided remotelyfrom the base stations or provided at the base station. Any of thenetwork controller devices 110, 112 and 114 may be a non-dedicateddevice that provides NRC functionality among others. In anotherembodiment, an NRC is a Self-Organizing Network (SON) server. In anembodiment, any of the network controller devices 110, 112 and 114and/or one or more base stations 102 may function independently orcollaboratively to implement processes associated with variousembodiments of the present disclosure.

In accordance with a standard GSM network, any of the network controllerdevices 110, 112 and 114 (which may be NRC devices or other devicesoptionally having NRC functionality) may be associated with a basestation controller (BSC), a mobile switching center (MSC), a datascheduler, or any other common service provider control device known inthe art, such as a radio resource manager (RRM). In accordance with astandard UMTS network, any of the network controller devices 110, 112and 114 (optionally having NRC functionality) may be associated with aNRC, a serving GPRS support node (SGSN), or any other common networkcontroller device known in the art, such as an RRM. In accordance with astandard LTE network, any of the network controller devices 110, 112 and114 (optionally having NRC functionality) may be associated with aneNodeB base station, a mobility management entity (MME), or any othercommon network controller device known in the art, such as an RRM.

In an embodiment, any of the network controller devices 110, 112 and114, the base stations 102, as well as any of the UE 108 may beconfigured to run any well-known operating system, including, but notlimited to: Microsoft® Windows®, Mac OS®, Google® Chrome®, Linux®,Unix®, or any mobile operating system, including Symbian®, Palm®,Windows Mobile®, Google® Android®, Mobile Linux®, etc. Any of thenetwork controller devices 110, 112 and 114 or any of the base stations102 may employ any number of common server, desktop, laptop, andpersonal computing devices.

FIG. 2 illustrates a block diagram of an NRC 200 that may berepresentative of any of the network controller devices 110, 112 and114. Accordingly, NRC 200 may be representative of a Network ManagementServer (NMS), an Element Management Server (EMS), a Mobility ManagementEntity (MME), or a SON server. The NRC 200 has one or more processordevices including a CPU 204.

The CPU 204 is responsible for executing computer programs stored onvolatile (RAM) and nonvolatile (ROM) memories 202 and a storage device212 (e.g., HDD or SSD). In some embodiments, storage device 212 maystore program instructions as logic hardware such as an ASIC or FPGA.Storage device 212 may store, for example, location data 214, cellpoints 216, and tier relationships 218.

The NRC 200 may also include a user interface 206 that allows anadministrator to interact with the NRC's software and hardware resourcesand to display the performance and operation of the system 100. Inaddition, the NRC 200 may include a network interface 206 forcommunicating with other components in the networked computer system,and a system bus 210 that facilitates data communications between thehardware resources of the NRC 200.

In addition to the network controller devices 110, 112 and 114, the NRC200 may be used to implement other types of computer devices, such as anantenna controller, an RF planning engine, a core network element, adatabase system, or the like. Based on the functionality provided by anNRC, the storage device of such a computer serves as a repository forsoftware and database thereto.

Neighbor tier counting is facilitated by establishing boundaries forindividual cells. Determining the coverage area of each cell facilitatesestablishing cell boundaries. There are a number of ways in which thiscan be accomplished.

Cell boundaries can be established using an RF planning tool or frommeasurements in a deployed network, such as drive test measurements ordata from a geolocation tool. RF planning tools can make a determinationof which cells are first tier neighbors of each other. Second, third andsubsequent tier neighbors may be determined through variousrelationships. However, this level of RF planning tool information isnot always available to a SON tool, and even when it is, the amount oftime and resources, including processor resources, for providing suchinformation makes it difficult to provide current coverage informationin a timely manner. In addition, in the case of a customer trial,operators may be reluctant to provide information from their planningtools, which typically includes sensitive data.

Drive test and Geolocation data could be used to make determinations ofcell coverage area. However, there are drawbacks to making tierdeterminations using drive test or geolocation information. For example,such information requires that networks be already deployed. Howeversome SON algorithms (e.g., neighbor list initialization) use neighbortier separation data prior to a cell being deployed. Thus, this data isnot available in some situations.

Drive test data requires physical presence in various geographiclocations which may not be practically accessible. Accordingly, drivetest data is generally not available for all parts of the network. Inaddition, an operator may not have deployed a geolocation solution intheir network.

On the other hand, SON tools are generally provided with cell siteinformation such as cell location including cell latitude and longitude,whether cell is deployed indoors or outdoors, antenna azimuth (pointingdirection), and antenna height information. Using this informationalone, it is possible to make an estimate of cell coverage areas and usethis information to determine cell boundaries, first tier neighborcells, etc. Embodiments of such a process and a system that implementsthe process are provided by this disclosure.

FIG. 3 illustrates a general process 300 for determining neighbor tierrelationships for cells. Elements of process 300 will be explained inmore detail with respect to subsequent figures and processes.

In process 300, shapes are established at S302 for cell sites, which maycorrespond to the location of a base station, such as a cellular towerfor a macrocell. The cell site shapes may be used to establish cellsS304, which may be represented as points, shapes, or both in variousembodiments. For example, a cell point may be a centroid of a cellshape, a base station location for cases such as a femtocell with anomnidirectional antenna, or a point a certain distance along an azimuthfrom a base station. In an embodiment with an omnidirectional antenna, asite shape may be the same as a cell shape. After cells are established,neighbor tier relationships between cells are determined at S306.

FIG. 4 shows a process S400 for establishing a shape around a cell site.Locations for cell sites in a cellular network are determined at S402. Alocation for a cell site may be latitude and longitude values for thecell site. The cell site locations may be maintained in a database,which may be a pre-existing database of a SON server in a specificembodiment. Such a database may be updated as new cell sites aredeployed, and processes according to embodiments of this disclosure maybe performed periodically so that neighbor tier relationships areaccurate as the network evolves.

Neighbor tier relationships may be stored in a memory by one or morenetwork device. For example, neighbor tier relationships may be storedby a base station 104 and/or a network resource controller 200 for usewith various network operations.

Network planning teams generally select cell sites to have a coveragearea in all directions around the cell site. This is particularly truefor Macro cell deployments. Typically, the locations closest to a cellsite are served by that cell site.

Cell types for the cell sites are determined at S404. Various types ofcells have different characteristics, and an embodiment may account forone or more characteristic when creating a shape for the site at S406.For example, the coverage area of a femtocell is substantially smallerthan the coverage area of a macrocell, so different techniques may beemployed when establishing a femtocell shape compared to establishing amacrocell shape. Examples of how cell types may influence establishingshapes S406 are provided in more detail below with respect to FIGS. 11A,11B and 13A.

Shapes are established around the site locations at S406. Establishingshapes S406 will be explained with respect to FIG. 5A, which showsshapes in a regular (e.g. evenly spaced) deployment, and FIG. 5B, whichshows a deployment with varying site density. The shapes in FIGS. 5A and5B are Voronoi polygons established using Voronoi diagrams.

For a given set of points, a Voronoi diagram divides an area intoregions around a plurality of points, or seeds, in such a way that eachpoint in a region is closest to its seed. If the seeds are cell sites,then resulting regions are polygons that provide a useful approximationof the coverage area of a cell site. While the resulting polygons arenot exact representations of the coverage area of each site, theboundary of the polygons can be used as indication of the first tierneighbor sites of each site.

An example of a set of sites 502 and the Voronoi polygons 504 for thosesites is shown in FIG. 5A. Depending on the layout of the sites 502, thepolygons may have various numbers of sides. Highly efficient algorithmshave been developed for creating Voronoi polygons around data points,which can be employed in embodiments of this disclosure.

FIG. 5B shows a Voronoi diagram of a variable density site scenario.This example is representative of a high density site deployment aroundtwo small urban areas, with rural sites in between.

FIG. 5B illustrates an advantage of an embodiment of this disclosureover a distance-based approach. While a distance-based approach mayrecognize that site 502 a is a neighbor of site 502 b, thedistance-based approach may not recognize that site 502 c is a neighborof site 502 b because there is a substantial distance between them.However, for mobility purposes, site 502 c is a first-tier neighbor ofsite 502 b, and cells associated with site 502 c will accept handoversfrom cells associated with site 502 b.

In the Voronoi diagrams of FIG. 5A and FIG. 5B, first tier siteneighbors are those that share a common polygon edge. Second tierneighbors are those that have a common first tier neighbor, and so on.

Instead of calculating polygon edges, the first tier neighbors can bedetermined via Delaunay triangulation. For a first point (site) 502,Delaunay triangulation directly provides the points (sites) 502 thathave Voronoi polygon edges that are adjacent to the polygon edges of thefirst point.

FIG. 6 shows a process 600 for determining tier relationships betweencells. In process 600, distances between site points are determined atS602. FIG. 7A shows the three cell sites 502 a, 502 b and 502 c fromFIG. 5. In FIG. 7A, the distance between cell sites 502 a and 502 b isrepresented by line 710 a, and the distance between sites 502 b and 502c is represented by line 710 b.

In an embodiment, determining distances between site points may beaccomplished by performing Delaunay triangulation to all site locationsin a network area. The resulting mesh from a Delaunay triangulation ofthe site points may effectively determine distances between allneighboring cell sites, where a length of a triangle leg between pointscorresponds to a distance between the points.

The nearest neighbor site for each cell site may be determined at S604.Such a determination may be made, for example, by comparing the lengths(distances) of all triangle legs from a Delaunay triangulation with avertex at a target cell site. For example, if cell site 502 b of FIG. 7Ais a target site, then comparing 710 a to 710 b returns a result thatthe nearest neighbor is cell site 502 a. For convenience, thisdisclosure may represent the distance to the nearest neighbor of atarget cell site as variable dminSite.

A typical cellular telecommunications network includes a large number ofeNodeB base stations as cell sites. An eNodeB base station is typicallyconfigured to provide three co-sited cells for a given set offrequencies to establish 360 degrees of coverage around the basestation. Accordingly, an eNodeB typically has three antennas to servethe co-sited cells, and each antenna has an azimuth that is separatedfrom azimuths of the other two antennas.

Cell points 714 are established along azimuth lines of each cell site502 at S606. If cell points are chosen so that they are equidistant fromthe site location, then when Voronoi polygons are subsequently providedfor the cell points, the resultant polygon edges between adjacent cellsat the same site will bisect the azimuths of each cell. If the cellpoints are close to the site point, then the resulting polygons from theVoronoi diagram of the cell points are similar to segmented versions ofthe site polygons. If the cell points overlap the site point, then thepolygons of the cell points will be very similar to a polygon of thesite point.

A suitable distance for locating cell points along azimuth lines at S606may be determined by finding the closest first tier site and taking afraction of this distance. In general, the fraction should be less than0.5, which is half of the distance dminSite between the site and itsclosest first tier neighbor site, in order to avoid locating the cellpoint in the coverage area of an adjacent cell. Values from 0.05 to 0.3have been found to work well in practice. Each cell point is then setalong the azimuth line of that cell, where the distance from the site502 is the chosen fraction of the distance between the site 502 and thesite of its closest neighbor (dminSite).

FIGS. 7B and 7C illustrate some of the elements of steps S604 and S606.For example, FIG. 7B shows a polygon 504 a for cell site 502 a, and line710 a represents the distance dminSite between cell site 502 a and cellsite 502 b as shown in FIG. 7A. In addition, FIG. 7B shows cell azimuthdirections 712, which are represented by arrows oriented in therespective pointing directions of three corresponding antennas of cellsite 502 a.

FIG. 7C shows a result of performing process S606 to the embodiment ofFIG. 7B. In particular, cell points 714 a, 714 b and 714 c areestablished at distances along the azimuth lines 716 a, 716 b and 716 c,respectively. The distances used in FIG. 7C correspond to about 0.25, or25%, of the original distance dminSite of minimum distance 502 b.

In another embodiment, different cell points of a cell site may belocated at different distances from the cell site origin. For example,consider FIG. 7A, in which cell site 502 b is neighbored by site 502 ain one direction and site 502 c in another direction. Cell site 502 c issubstantially farther from site 502 b than site 502 a. In order toaccount for this discrepancy, an embodiment may use different dminSitevalues for each azimuth of a cell site 502.

For example, an embodiment may determine a nearest neighbor fromneighboring sites that are found within an arc segment centered aroundan azimuth line and projecting outward from the origin cell site, anddetermine different dminSite values based on distances to neighbors foreach separate azimuth. Such an embodiment may be employed, for example,when neighbor tiers are counted using ray trace techniques or othertechniques that are more sensitive to cell point shapes than relationaltechniques such as edge sharing techniques.

Shapes are created around cell points at S608. Creating shapes aroundcell points may be performed by establishing Voronoi polygons using cellpoints as the seed values for the polygons.

FIGS. 8A and 8B show a difference between a Voronoi diagram for cellsites and a Voronoi diagram for cell points. In particular, FIG. 8A is aVoronoi diagram showing Voronoi polygons around a plurality of cellsites. FIG. 8B is a cell point diagram that was established bydetermining distances to nearest neighbors for each cell site,projecting azimuth values onto the cell site locations of FIG. 8A, andlocating cell points at a fraction of 0.25 of the minimum neighbordistance dminSite along the azimuth lines for each site. In other words,FIG. 8A represents a result of an embodiment of a process 400, whileFIG. 8B represents a result of an embodiment of step S608 of processS600.

Depending on the technique employed for tier counting, certainembodiments may not perform step S608. For example, triangulationtechniques establish links between cell points, so it may not benecessary to establish shapes for cell points when tiers are countedusing triangulation. In contrast, ray trace and shared edge techniquesuse polygons for cell points to determine tier relationships.

Cell points may be connected to one another at S610. In an embodiment,each cell point is connected to its nearest neighbors using Delaunaytriangulation. Delaunay triangulation is a useful technique forestablishing connections between neighboring cells in the same way thatnetwork engineers understand neighbor relationships. Delaunaytriangulation is useful to automate a process that returns meaningfuland accurate results.

Tier relationships between cell points are determined at S612.Embodiments of determining tier relationships are discussed in detailbelow.

FIG. 9 illustrates an embodiment of a process 900 for determining tierrelationships between cells that is a different from process 600 of FIG.6. At S902, azimuth values are determined for cell sites. As discussedabove, a macrocell site typically serves three cells, so when a site isa macrocell site, S902 may determine three azimuth directions. In anembodiment, azimuth values for a cell site are determined by retrievingdata from a database of azimuth directions.

The azimuth directions are located on a site polygon at S904. FIG. 10Ashows azimuths 1004, which are represented as rays emanating indifferent directions from the cell site location 1002, projected onto asite polygon 1006. In an embodiment, azimuth lines 1004 are extended tothe edges of polygons 1006. However, the angular component of theazimuth is used at S906, so embodiments may project rays emanating indirections from cell sites 1002 instead of lines with two points.Although there are three arrows in azimuths 1004 which represent atypical macrocell site, other macrocell sites may serve differentnumbers of cells, so the numbers of azimuth rays may be adapted tocorrespond to the number of cells served by a site within a particulartechnology and frequency range.

As seen in FIG. 10B, angles between two adjacent azimuth rays 1004 arebisected by lines 1008 at S906, which are shown as dashed lines in thefigure. Bisecting the azimuths 1004 can be may be accomplished bydetermining an angle between two azimuth rays, and establishing line1008 at an angle that is about halfway between the two azimuth rays,with endpoints of the line at the cell site 1002 and an edge of the sitepolygon 1006. The polygons 1010 that result from S906, which includelines defining the edges of site polygon 1006 and the bisected azimuthlines 1008, are representative of cells that are served by cell site1002. The cell polygons around cell site 1002 are represented aspolygons 1010 a, 1010 b, and 1010 c in FIG. 10B.

In an embodiment, a centroid 1012 is established for each respectivecell polygon 1010 at S908. The centroid 1012 for a cell polygon 1010 mayrepresent a cell point for the polygon.

After centroids 1012 are established at S908, polygons may beestablished for the cell points 1012 at S910 by creating a Voronoidiagram of the cell points. However, other embodiments may not performS910, and may count tiers based on cell polygons 1010 from S906 orcentroids 1012. Similarly, cell points may optionally be connected atS912 by Delaunay triangulation depending on the manner in which tiersare counted. Tiers are then counted at S914, for example by countingshared edges, ray tracing, etc.

In FIGS. 10A and 10B, each base station provides three cells, asindicated by the three azimuth directions 1004. However, some cell sitesdo not have three antennas. For example, sites for femtocells may havean omnidirectional antenna, while other cell sites may provide othernumbers of cells. Accordingly, processes and systems according to thisdisclosure may determine a type of base station associated with celltypes and apply rules to process 600 or process 900 that are specific tothe cell type.

Processes 600 or 900 may be applied to all cells in a network. This maylead to an over-estimate of the number of tiers between cells in somecases. When smaller cells with less than 360 degree coverage, or indoorcells are also deployed in a network, then different processes may beapplied when establishing shapes for such cell sites at S406. Forexample, in some embodiments, different shapes or weighting may be usedfor certain types of cells.

For example, if there is a Pico cell between two Macro cells, thentypical a Voronoi diagram makes the Pico cell first tier neighbors ofeach Macro cell, but may make the macro cells second tier neighbors ofeach other, when they should be first tier neighbors. Such an embodimentis shown in FIGS. 11A and 11B.

FIG. 11A shows an embodiment of a Voronoi diagram of shapes around cellpoints 1108. The shape 1106 in the middle represents a pico cell withlow transmit power, and the polygons 1102 and 1104 on the left and rightrepresent macro cells. The resulting Voronoi diagram is as shown in FIG.11A.

The situation in FIG. 11A may lead to an over-estimate of the number oftiers between two cells in some cases. FIG. 11A shows a result ofapplying Voronoi polygons to macrocells 1102 and 1104 as well aspicocell 1106. However, the relationships in FIG. 11A may not accuratelyrepresent relationships between the cells from a user mobilityperspective. For example, while FIG. 11A requires transiting across cell1106 to move from cell 1102 to cell 1104, in an actual physical space,UE may handover from cell 1102 directly to cell 1104 without interactingwith picocell 1106.

FIG. 11B illustrates a picocell 1106 located between two macrocells 1102and 1104. As shown in FIG. 11B, the polygon representing cell 1102shares edges with the polygon representing cell 1104. In an embodiment,sharing a shape edge indicates a first-tier neighbor relationship.Accordingly, the embodiment of FIG. 11B is a more accuraterepresentation of cell tier relationships than FIG. 11A. In anotherembodiment, when the cell site 1108 for picocell 1106 is closer to acell site of a macrocell, the circle representing picocell 1106 in FIG.11B may be located entirely within an area of a macrocell shape,representing a relationship in which the picocell is only a first tierneighbor to that macrocell.

FIG. 11B shows an example of establishing a circular shape for a cellsite at S406 when S404 determines that the cell type of cell site 1108is a picocell. The shape used to represent omnidirectional antennas maybe a circle. Other embodiments may use various shapes to more accuratelyrepresent coverage areas of different types of base stations anddeployment scenarios. Other shapes that may be used for these cellsinclude a wedge shape, a triangle, a circle, an oval, and combinationsof these and other shapes.

Specific shapes may be applied to certain cell types and deploymentscenarios separately from creating polygons for other cells using aVoronoi diagram at S406. For example, an embodiment of S406 may includefirst establishing Voronoi polygons for macrocells, and second applyingspecific shapes, which may be weighted polygons.

In some embodiments, weighting may be applied based on a cell type or adeployment scenario. Weighting may be applied to a general polygon froma Voronoi diagram, or a specific shape for a cell type. Factors that maybe used to apply weighting to a shape include the type of cell, thetransmit power, the antenna height, and location characteristics, suchas whether the cell site is indoors or outdoors.

Weighting may be applied in many different ways. In an embodiment, cellweights may be scaled to a coverage area or transmit power of a celltype. For example, a macrocell may be weighted more than a microcell,which may in turn be weighted more than a picocell. Othercharacteristics that may be assigned different weights include power,antenna height, and environment. For example, higher power cells may beweighted more than lower power cells, higher antenna heights may beweighted more than lower antenna heights, and outdoor deployments may beweighted more than indoor deployments. Persons of skill in the Art willrecognize that other cell characteristics can influence the size ofrepresentative shapes in other embodiments.

In another embodiment, one or more cell shape may be established using apower diagram. The size of shapes in the power diagram may be adaptedaccording to weighting based on cell characteristics as described above.The weighting may be applied through a multiplicatively weighteddiagram, and additively weighted diagrams may be suitable as well.

Other cell characteristics that may be evaluated to determine a shapeand/or a size of a shape include the Radio Access Technology (RAT) andfrequency layers of a cell. In general, the neighbor tiers will bedetermined for cells of a particular RAT (e.g., GSM, UMTS, LTE) thatoperate on the same frequency. However, depending on the application,neighbor tier counting can also be implemented for cells of differenttypes. For example, first tier inter-RAT neighbors may be determinedusing the approaches in this disclosure by calculating the Delaunaytriangulation and/or Voronoi polygons for cells of another technology.

FIG. 12 illustrates a process 1200 for determining a tier relationshipbetween two cells. FIG. 12 is an example of counting tiers, andcorresponds to S914, S612 and S306.

Shapes are established at S1202. In one embodiment, shapes areestablished in accordance with S608 as Voronoi polygons around cellpoints. In another embodiment, shapes are established by bisectingazimuth lines of cell sites in accordance with S910. Accordingly,process 1200 may be performed using shapes that were established fromvarious embodiments.

Cells for which tier relationships are determined are selected at S1204.Tier relationships may be determined for all cells in a network, forcells in a particular area, or for two or more specific cells. Thus, twoor more cells may be selected at S1204.

In an embodiment, when a new cell is installed, tier relationships forthe new cell and its neighbors may be determined. In addition, a newcell may affect tier relationships for pre-existing cells in an areaaround the new cell. Therefore, tier relationships for all cells in anarea around a new cell may be selected at S1204.

One way of counting the tiers between neighbor cells is to find theminimum number of cells that have to be traversed to get from thecoverage area of a first cell to the coverage area of a second cell.This may be accomplished, for example, by counting transitions betweencells at S1206. An embodiment of counting transitions between cells isshown in FIG. 13A.

FIG. 13A shows a plurality of cell shapes 1302 that are establishedaround cell points 1304. In FIG. 13A, neighbor tier relationships aredetermined between a first cell corresponding to cell shape 1302 a and asecond cell corresponding to cell shape 1302 c. There are two cell shapeboundaries 1306 between first cell shape 1302 a and second cell shape1302 c. Each of the cell shape edges 1306 corresponds to a transitionbetween adjacent cells. Therefore, performing S1206 on cells 1302 a and1302 b results in a single transition, or cell shape edge 1306 a,between the cells, so cell 1302 a is a first tier neighbor of cell S1302b.

Similarly, two cell shape edges 1306 a and 1306 b lie between cellshapes 1302 a and 1302 c. Accordingly, the cell that corresponds to cellshape 1302 a is a second tier neighbor of the cell that corresponds tocell shape 1302 c. In an embodiment, an efficient algorithm such asDijkstra's algorithm may be employed to determine a minimum number ofedges between selected cells at S1206.

After tier relationships are determined by counting transitions atS1206, the tier relationships are stored in a database at S1208. Thetier relationships may be transmitted to and stored by networkequipment, where it may subsequently be used to perform a variety ofnetwork activities. While tier relationships may be stored by a SONserver at S1208, tier relationships may also be stored by other networkequipment such as an RRM, a base station, and UE.

FIG. 13B shows another embodiment of process 1200 that includes twovariations from three sectored macrocells. In particular, the basestation that serves cell 2 uses an omnidirectional antenna, so cell 2 isrepresented as a single polygon around cell site 1304. Cell 1 isassociated with a three sector macrocell site 1304 c, but cells 3 and 4are associated with a cell site 1304 a that has six antennas thatprovide service for six respective cells. Therefore, six cell polygonsare established around cell site 1304 a.

Applying process 1200 to FIG. 13B, cells 1 and 4 are selected at S1204.S1206 counts three transitions 1306 a, 1306 b and 1306 c between cells 1and 4. The transitions are defined by cell shape boundaries. The tierrelationship between cells 1 and 4 corresponds to the number oftransitions, or boundaries, between the cells, so cell 1 is establishedas a third tier neighbor of cell 4.

FIG. 14 shows a process 1400, which is another embodiment of determininga tier relationship between cells. Establishing cell shapes S1402 andselecting cells S1404 may be performed in the same fashion as S1202 andS1204 above, so a detailed description of these elements will be omittedfor the sake of brevity.

The selected cells are connected at S1406. For example, FIG. 15 shows anexample of a Voronoi diagram of a plurality of cell shapes 1502, inwhich cell shape 1502 a and cell shape 1502 c correspond to the selectedcells. The selected cells are connected by a line 1508, which FIG. 15shows as being projected onto a Voronoi diagram of cells in a network.

Although FIG. 15 shows the end points of line 1508 being cell points1502, the end points of the line may be different in other embodiments.For example, in an embodiment in which cell site shapes are divided bylines bisecting azimuth directions, such as the embodiment shown in FIG.10B, end points of a connecting line may be established at cell sites1002. In another variation, centroids 1012 of cell shapes 1010 may beused as endpoints.

Intersections are counted at S1408. In particular, intersections betweenconnection line 1508 and underlying cell shapes are counted. In FIG. 15,line 1508 intersects cell shapes 1502 a, 1502 b and 1502 c, or threecell shapes. The tier relationship between selected cells is N−1, whereN represents the number of cell shapes intersected by the line 1508between cell points. Therefore, the cells corresponding to cell shapes1502 a and 1502 c are determined to be second tier neighbors of oneanother. Tier data is then stored at S1410.

FIG. 16 shows a process 1600, which is another embodiment of determininga tier relationship between cells. Cell points are determined at S1602as discussed above, and the cell points are connected at S1604.

FIG. 17 shows an embodiment in which cell points 1704 are connected toone another by lines 1710. In an embodiment, cell points may beconnected to each other by performing Delaunay triangulation on an arrayof cell points. Delaunay triangulation is a useful technique forconnecting cell points by establishing short paths between the cellpoints.

Cells for which a tier relationship is being determined are selected atS1606. In the embodiment of FIG. 17, cells 1702 a and 1702 c areselected. A number of connections between these cells is then determinedat S1608. In particular, a least number of connections between cells maybe determined.

For example, FIG. 17 shows that cell point 1704 a can be connected tocell point 1704 c through two connections 1710 a and 1710 b. Countingthe number of connections at S1608 determines that two connections arepresent between the cell points. The least number of connections betweencell points corresponds to a tier relationship between the cells, soprocess 1600 would determine that the cell associated with cell point1704 a is a second tier neighbor of the cell associated with cell point1704 c. This relationship may be stored at one or more device at S1610.

Depending on the activities that tier relationship data supports, it maybe sufficient in some embodiments to know the exact number of tiersbetween cells when the cells are less than or equal to N tiers apartfrom each other, where N is an integer. If the cells are more than Ntiers apart, then it may be sufficient to know they are more than Ntiers apart, without knowing exactly how many tiers apart the cells are.In this case, it may be more efficient to pre-compute all the neighborswithin the N tiers for each cell.

An example of a process 1800 for identifying neighbor relationships lessthan a certain value for a source cell is shown in FIG. 18. In process1800, the cutoff value for tier relationships is 10.

Integer N is set to 0 at S1802. A first empty set that will be used tohold the first N tier neighbors is created at S1804. The source cell isadded to the first set with a tier count attribute of 0 at S1806.

For cells already in the first set that have a tier count attributeequal to N, their first tier neighbors are placed into a second set at1808. A second set is created for first tier neighbors of cells alreadyin the first set that have a tier count attribute equal to N at S1808.So first tier neighbors of the source cell will be placed in the secondset when N=0. Cells in the second set that are not already in the firstset are added to the first set at S1810 with a tier count attribute ofN+1, and N is incremented by +1 at S1812. S1808 to S1812 are repeateduntil a specified tier value is reached, which is 10 at S1814 in FIG.18. Accordingly, process 1800 counts a number of first tierrelationships for a first cell, and when compared to a second cell,effectively counts a number of first tier relationships between thefirst cell and the second cell.

Thus, performing process 1800 will identify all cells that have aneighbor tier relationship of less than or equal to a certain value fora source cell. Process 1800 is provided for illustrative purposes, andother specific embodiments are possible.

FIG. 19 shows another embodiment of a process 1900 for determining atier relationship between cells. The shapes in process 1900 are circles,or rings. Accordingly, process 1900 may be referred to as a ringprocess.

A source location is selected at S1902. In an embodiment, the sourcelocation may be selected by selecting a cell point such as a cell point714 a of FIG. 7C, or by selecting a cell site such as cell site 502 a ofFIG. 7C. A cell site may be selected when the cell site is associatedwith an omnidirectional antenna, or for specific applications such asANR optimizations.

The distance to a nearest neighbor location is determined at S1904. Inan embodiment, the nearest neighbor is a cell that is the closestdistance to the source cell that uses the same UTRA Absolute RadioFrequency Channel Number (UARFCN) layer as the source. When the sourcelocation is a cell point, the distance may be the distance to theclosest cell point that is associated with a different cell site.

However, in other embodiments, cell site locations may be used as sourcelocations. Such an embodiment is shown in FIG. 20, which shows adistance 2006 between source cell site 2002 and nearest neighboring cellsite 2004. In an embodiment, a cell site may be used as a proxy for oneor more cells that are associated with such a cell site. When the sourcelocation is a cell site, the distance may be the distance to the closestcell site that uses a same UARFCN as the source cell site.

The distance 2006 may be converted to a radius value of a ring 2008 bydividing the distance by two. The ring 2008 may be established at S1908by creating a circle centered at source location 2002 with a radius fromS1906. S1902 to S1908 may be repeated as many times as desired forlocations in a wireless communications network.

A relationship between a source location 2002 and another location isdetermined at S1910. The relationship may be determined, for example, byestablishing a line between a source location 2002 and a targetlocation, and counting a number of rings 2008 that the line traversesother than the ring of the source location. In such an embodiment, anumber of tiers between the source and target locations may be thenumber of rings other than the source ring.

Process 1900 is a useful alternative to using raw distance values toclassify relationships between cell sites and/or individual cells. Rawdistance does not account for variations in density, while process 1900can establish relationships that do account for density. As such,process 1900 and other processes of this disclosure are more robust anduseful than raw distance to a variety of cellular network technologies.In a specific embodiment, process 1900 may be used to determineunnecessary or problematic neighbor relations between cells by removingneighbor relations for which the number of tiers from S1910 is greaterthan a threshold value.

Triangle Edge Removal

The accuracy of neighbor tier determination from triangulation can beimproved by removing certain triangle edges from an initial set oftriangles. Initial Delaunay triangulation may not identify optimal tierrelationships for cells at the outer edges of a network and isolatedcells in the middle of a large network. In these cases, Delaunaytriangulation may identify cells as being first tier neighbors thatwould not otherwise be considered to be first tier neighbors by networkengineers.

While such cells may geometrically meet the criteria to form a Delaunaytriangle, they may be too distant from each other to be considered firsttier neighbors. In other cases, such cells may be at the edge of anetwork, where cells are actually multiple tiers away from each other,but the triangulation identifies an erroneous first tier relationship.

The following disclosure describes a system and method that can be usedto examine triangles formed for a given cellular network and todetermine whether any of these triangles contain any edges or in otherwords incorrect first-tier neighbor assignments. There are at least twoways to remedy this problem, either through the complete removal of thetriangle meeting any of the criteria explained below or through removalof only the one or more edges of a given triangle that represent thoseincorrect first tier neighbor assignments. Empirical testing hasestablished that removing particular edges established by Delaunaytriangulation results in highly accurate and efficient determination ofneighbor tier relationships.

FIG. 21 illustrates a method 2100 for determining neighbor relationshipsaccording to an embodiment of the present disclosure. At S2102, cellpoints of a plurality of cell points are connected using Delaunaytriangulation. The cell points may be cell points 1504 or cell points1704 as explained with respect to FIGS. 15 and 17 above. The cell pointsmay be established using methods explained in this disclosure, or anyother methods determine points that represent a geographical location ofa cell in a wireless network. FIG. 22 illustrates cell points in awireless telecommunications network that are connected to one another byDelaunay triangulation.

Applying triangulation at S2102 leads to a set of triangles, where eachedge represents a connection between two first-tier neighboring cells.Depending on the location of a given cell, each edge may belong toeither only one triangle or may be shared by two triangles. Thefollowing elements S2104 to S2110 of process S2100 provide criteria thatmay be used to identify unwanted or incorrect edges of these triangles.

A distance-based criterion is applied to the Delaunay triangles at S2104in order to identify edges of the Delaunay triangles that representincorrect neighbor tier relationships. In particular, the edges thatrepresent incorrect neighbor tier relationships are edges between afirst cell and a second cell where a handover operation from the firstcell to the second cell is not expected to occur.

For a given set of points, Delaunay triangulation maximizes the minimumangle of all the angles of the triangles in the triangulation and ingeneral avoids the formation of so-called “skinny” triangles. However,when applied to certain network areas such as the outer edges of acellular network, Delaunay triangulation can result in “skinny”triangles. Delaunay triangulation may link two cells on the edges of anetwork that, despite having a direct line of sight on each other, havemultiple cells between them, and would normally not be considered to befirst-tier neighbors.

A first angle-based criterion is applied to the Delaunay triangles atS2106. In an embodiment, the first angle-based criteria is a middleangle criterion in which the largest edge of triangles whose middleangle is less than a threshold value is identified as a candidate forremoval.

A second angle-based criterion is applied to the Delaunay triangles atS2108. In an embodiment, the second angle-based criterion is a minimumangle criterion in which the largest edge of triangles whose minimumangle is less than a threshold value is identified as a candidate forremoval.

A third angle-based criterion is applied to the Delaunay triangles atS2110. In an embodiment, the third angle-based criterion is aratio-based criterion in which a ratio of the smallest angle of atriangle to the largest edge of the triangle is used as a criterion foridentifying candidate edges for removal.

The edges that are candidates for removal may be stored in a memory. Thememory may be a memory such as memory 202 or storage device 212 ofnetwork resource controller 200. The candidates may be stored in amemory in order to perform further operations before removing the edges,such as determining whether an edge that is marked for removal is sharedwith another triangle. Such an operation is explained in further detailin process 3200.

FIG. 23 illustrates the network diagram of FIG. 22 in which triangleedges identified at S2104, S2106, S2108 and S2110 are represented asgray or lower weight lines.

Edges are removed from the Delaunay triangles at S2112. The edges thatare removed may be the edges that are identified by applying distance orangle criteria at one or more of S2104, S2106, S2108 and S2110.

FIG. 24 illustrates the network diagram of FIG. 23 from which theidentified edges have been removed. The remaining lines in FIG. 24represent first-tier relationships between cells that correspond to thecell points.

Such relationships may be used by a cellular network to add or removeneighbors from neighbor lists. For example, when a neighbor list for agiven cell includes a neighbor cell that is connected to the given cellthrough a neighbor relationship that is determined to be incorrect byprocess 2100, the neighbor cell may be removed from the neighbor list ofthe given cell and possibly blacklisted. In another embodiment, cellsthat are connected to one another by lines of FIG. 24 may be added toeach other's neighbor lists. Persons of skill in the art will recognizethat other uses may be made of the neighbor relationships determined byprocess 2100 and shown in FIG. 24.

FIG. 25 shows a process 2500 for applying a distance-based criterion todetermine edges that are candidates for removal. Process 2500corresponds to element S2104 of process 2100 described above. Adistance-based criterion may applied because when two cells areseparated by a great distance, they are not effectively first-tierneighbors of one another. In particular, when the distance between twocells is too great, a handover operation may not be expected to occurbetween the two cells.

Distances for the edges of triangles in a triangulated network diagramare determined at S2502. The distances may be linear distancesrepresenting the separation in space between cell points, such a numberof kilometers between the cell points. In some embodiments, depending onthe nature of the network diagram, the distance may be a number ofpixels in an edge or some other scaled distance value.

The distance values are compared to a threshold value at S2504. Thethreshold value may be, for example, 5 kilometers, 15 kilometers, 20kilometers, or 25 kilometers. Values outside of this range may identifytoo many or too few edges for removal, limiting the effectiveness of theprocess.

In an embodiment, the distance value may be different between particulargeographical areas. For example, the distance at which a handover mayoccur is less for a highly dense urban area such as Manhattan than thedistance at which a handover may occur in a low density rural area.Accordingly, the threshold distance value may be different for differentgeographical areas in a network.

Edges that are greater than the threshold value are marked as removalcandidates at S2506. FIG. 26 illustrates a zoomed-in perspective of aportion of the network diagram shown in FIG. 23. In FIG. 26, edges 2602that connect cell point 648 exceed the threshold distance value and aremarked for removal as shown by the gray lines connecting cell point 648to cell points on the edge of a higher density portion of the network.Other edges 2602 that fail the distance criterion are similarlyindicated in gray on FIG. 26.

In an embodiment, marking an edge as a removal candidate may includerecording an identifier of the associated triangle in a database of“damaged” triangles. This database may be used in subsequent processesto determine whether to remove edges that are shared between twotriangles. Recording “damaged” triangles in a database may be performedfor all triangles for which an edge is marked for removal, regardless ofwhether the edge was identified for removal through a distance-basedprocess or an angle-based process.

FIG. 27 shows a process 2700 for applying an angle-based criterion todetermine edges that are candidates for removal. Process 2700corresponds to S2106 of process 2100 described above.

Values for angles of the triangles are determined at S2702. The valuesfor each triangle are compared to one another at S2704 to determinewhich angle is the middle angle. For example, with respect to thetriangle 2800 of FIG. 28, values of angles 2802, 2804 and 2806 arecompared to each other to determine that angle 2806 has the middle anglevalue.

The value of middle angle 2806 is compared to a threshold value, and ifthe middle angle is less than the threshold value, the longest edge 2812of the triangle 2800 is marked as a removal candidate. The thresholdvalue may be, for example, 10 degrees, 12 degrees or 15 degrees. Valuesoutside of this range may identify too many or too few edges forremoval, limiting the effectiveness of the process.

FIG. 29 shows a telecommunications network in which cell points havebeen connected to one another by Delaunay triangulation. FIG. 29magnifies an area of FIG. 26. Process 2700 has been applied to thetriangles of FIG. 29, and triangle edges 2902 were marked for removal at2708.

FIG. 30 shows a process 3000 for applying a minimum angle-basedcriterion to determine edges that are candidates for removal. Process3000 corresponds to element S2108 of process 2100 described above.

Values for angles of the triangles are determined at S3002. The anglesfor each triangle are compared to one another, and the minimum angle2802 is determined at S3004. A value of the minimum angle is compared toa threshold value at S3006, and if the angle is less than the thresholdvalue, then the longest edge 2812 of the triangle is marked for removalat S3008. Examples of threshold values that may be used at S3006 includetwo degrees, three degrees, and four degrees. Values outside of thisrange may identify too many or too few edges for removal, limiting theeffectiveness of the process.

Process 3000 has been applied to the triangles of FIG. 29. In thatfigure, edges 2904 were identified at S3006, and marked for removal atS3008.

FIG. 31 shows a process 3100 for applying a ratio-based criterion todetermine edges that are candidates for removal. Process 3100corresponds to element S2110 of process 2100 described above. Thiscriterion attempts to locate skinny triangles with emphasis on thosewith longer edges. Those are usually the ones more likely to beincorrect, involving cells that are too far from each other to beneighbors.

Values for angles of the triangles are determined at S3102. The anglesfor each triangle are compared to one another, and the minimum angle2802 is determined at S3104. The distance of the longest edge 2812 ofeach triangle is determined at S3106, and a ratio of the minimum angle2802 to the length of the longest edge 2812 is determined at S3108.

The ratio of the smallest angle 2802 to the length of the longest edge2812 is compared to a threshold value at S3110. When the length of thelongest edge 2802 is expressed in kilometers and the smallest angle isexpressed in degrees, a suitable threshold value may be 1.2, 1.5, or2.0. Values outside of this range may identify too many or too few edgesfor removal, limiting the effectiveness of the process. The longest edgeof a triangle whose ratio is less than the threshold value is marked asa candidate for removal at S3112.

While angle-based processes 2700, 3000 and 3100 have been described asmarking a longest edge of a triangle for deletion, in some embodiments,the two longest edges may both be marked as removal candidates. In anembodiment, an additional threshold may apply to this situation. Forexample, a length of a shortest edge 2814 may be compared to a thresholdvalue, a ratio between the two longest edges may be compared to athreshold value, a ratio of a longest edge to a shortest edge can becompared to a threshold value, etc. Other embodiments are possiblewithin the scope of the present disclosure.

FIG. 32 shows a process 3200 for removing edges from triangles withedges marked for removal. In an embodiment, process 3200 may be appliedat S2112.

At S3202, an edge of a triangle that is marked for removal isidentified. The edge may be any edge that is marked for removal as aresult of a distance or angle-based edge removal process, such asprocesses 2500, 2700, 3000 and 3100.

In some situations, an edge is shared between two triangles. Forexample, as seen in FIG. 33, while both of triangles A and B areindependently established between a plurality of cell points 3302,triangles A and B share edge 3312 as indicated by the thicker line.Accordingly, determining whether a marked edge is shared with anotheredge at S3204 would result in a “yes,” proceeding to S3208. When an edgethat is marked for removal is not shared with another triangle, thatedge is removed at S3206.

S3208 determines whether the shared edge is shared with a “damaged”triangle, which is a triangle that has at least one edge marked forremoval. In an embodiment, when the shared edge is shared with a damagedtriangle, the shared edge is removed at S3212. In another embodiment,the shared edge is only removed at S3212 when the specific edge ismarked as a candidate for removal in both triangles. When the edge isremoved, it is removed completely from the network. In other words, theshared edge is removed from both of the triangles that share the edge.

In still another embodiment, a triangle is only considered to be a“damaged” triangle when an edge has already been removed from thetriangle. An edge may have already been removed from a triangle, forexample, if a marked edge was determined not to be shared with anothertriangle at S3204, or if it failed the distance criterion of process2500. In such an embodiment, shared edges are removed at S3212.

Edge 3314 of triangle B of FIG. 33 is represented by a dashed line,which indicates that the edge is marked as a candidate for removal.Therefore, in an embodiment, shared edge 3312 would be removed from bothof triangles A and B at S3212. In another embodiment, because edge 3314is not shared between triangles A and B, it would be retained at S3210.

Elements of process 3200 can be seen in FIG. 29 and FIG. 26. FIG. 29shows a zoomed-in segment of the network of FIG. 26 along a geographicalboundary. For the cell site marked as cell 746, there are a number ofincorrect first-tier neighbor assignments due to skinny trianglesresulting from Delaunay triangulation. In this example, the edgeconnecting cell 746 with 684 is also part of the triangle connectingthese two cells with cell 648, as shown in FIG. 26.

As a result of the removal of edges in the triangle <648,746,684> ofFIG. 26, the remaining edge <746,684> are a “damaged” triangle.Therefore, when the angle criteria are applied and the same edge ismarked for removal from triangle <746,684,702>, it will also be removedfrom the “damaged” triangle and therefore the connection (or in otherwords, the neighbor assignment) between cells 746 and 684 will becompletely removed.

Embodiments of this disclosure may be used to determine which cellsshould be added to and removed from cellular neighbor lists; todetermine what priority should be assigned to cells on neighbor lists;to disambiguate reuse codes that are detected by mobile devices incellular networks; to set handover parameters and threshold values whichare used for operations such as handovers and load balancing operations;and to classify cell types in networks into core cells and edge cells,where core cells have a coverage area surrounded by many other cells'coverage areas and edge cells have coverage areas that extend wellbeyond the areas served by the core cells.

For example, a system for initializing neighbor lists for new cells incellular networks may use the first and second tier neighbors of a firstcell identified by embodiments of this disclosure as the cells to beplaced on the initial neighbor list of the first cell. Elements of thisdisclosure may affect a handover operation.

What is claimed is:
 1. A computer-implemented method for determiningneighbor tier relationships between cells in a wirelesstelecommunications network, the method comprising: establishing aplurality of cell points, each cell point representing a cell of aplurality of cells in the wireless telecommunications network; forming aplurality of triangles, the vertices of each triangle of the pluralityof triangles corresponding to respective cell points of the plurality ofcell points; applying a length-based or angle-based criterion toidentify triangle edges for removal, wherein the triangle edgesidentified for removal are longest edges of respective triangles;removing edges from a portion of the plurality of triangles; determiningneighbor tier relationships between the plurality of cells usingremaining triangle edges between the plurality of cell points; storingthe neighbor tier relationships in a first memory; and using theneighbor tier relationships for handovers between the plurality ofcells.
 2. The method of claim 1, wherein forming a plurality oftriangles includes performing Delaunay triangulation on the plurality ofcell points.
 3. The method of claim 1, wherein removing edges from aportion of the plurality of triangles includes comparing lengths oftriangle edges to a predetermined value, wherein triangle edges whoselengths exceed the predetermined value are the edges of the portion ofthe plurality of triangles that are removed.
 4. The method of claim 1,wherein removing edges from a portion of the plurality of trianglesincludes: determining a middle angle value of angles for each triangle;and comparing the middle angle value to a predetermined value, whereinlongest edges of the triangles whose middle angle values are less thanthe threshold value are the edges of the portion of the plurality oftriangles that are removed.
 5. The method of claim 1, wherein removingedges from a portion of the plurality of triangles includes: determininga minimum angle value of angles for each triangle; and comparing theminimum angle value to a predetermined value, wherein longest edges ofthe triangles whose minimum angles are less than the threshold value arethe edges of the portion of the plurality of triangles that are removed.6. The method of claim 1, wherein removing edges from a portion of theplurality of triangles includes: determining lengths of the longestedges of the triangles; determining minimum angles of the triangles;determining ratios between respective longest edge lengths andrespective minimum angles for each triangle; and comparing the ratios toa predetermined value, wherein longest edges of the triangles whoseratios are less than the threshold value are the edges of the portion ofthe plurality of triangles that are removed.
 7. The method of claim 1,further comprising: before removing the edges, identifying a pluralityof triangle edges as candidates for removal, and storing trianglesassociated with the candidate edges in a second memory; determiningwhether an edge of a first triangle that is a candidate for removal isshared with a second triangle; when the edge of the first triangle isshared with the second triangle, determining whether the second trianglehas an edge that has been removed or is a candidate for removal; andwhen the second triangle does not have an edge that has been removed oris a candidate for removal, retaining the shared edge.
 8. The method ofclaim 1, further comprising: before removing the edges, identifying aplurality of triangle edges as candidates for removal, and storingtriangles associated with the candidate edges in a second memory;determining whether an edge of a first triangle that is a candidate forremoval is shared with a second triangle; when the edge of the firsttriangle is shared with the second triangle, determining whether thesecond triangle has an edge that has been removed or is a candidate forremoval; and when the second triangle has an edge that has been removedor is a candidate for removal, removing the shared edge from the firstand second triangles.
 9. The method of claim 8, wherein, when the edgeof the first triangle is not shared with the second triangle, the edgeis removed.
 10. A network resource controller in a wirelesstelecommunications network, the controller comprising: a first memory; asecond memory; a processor; and a computer readable medium withexecutable instructions stored thereon which, when executed by theprocessor, perform the following operations: establishing a plurality ofcell points, each cell point representing a cell of a plurality of cellsin the wireless telecommunications network; forming a plurality oftriangles, the vertices of each triangle of the plurality of trianglescorresponding to respective cell points of the plurality of cell points;applying a length-based or angle-based criterion to identify triangleedges for removal, wherein the triangle edges identified for removal arelongest edges of respective triangles; removing edges from a portion ofthe plurality of triangles; determining neighbor tier relationshipsbetween the plurality of cells using remaining triangle edges betweenthe plurality of cell points; storing the neighbor tier relationships inthe first memory; and using the neighbor tier relationships forhandovers between the plurality of cells.
 11. The network resourcecontroller of claim 10, wherein forming a plurality of trianglesincludes performing Delaunay triangulation on the plurality of cellpoints.
 12. The network resource controller of claim 10, whereinremoving edges from a portion of the plurality of triangles includescomparing lengths of triangle edges to a predetermined value, whereintriangle edges whose lengths exceed the predetermined value are theedges of the portion of the plurality of triangles that are removed. 13.The network resource controller of claim 10, wherein removing edges froma portion of the plurality of triangles includes: determining a middleangle value of angles for each triangle; and comparing the middle anglevalue to a predetermined value, wherein longest edges of the triangleswhose middle angle values are less than the threshold value are theedges of the portion of the plurality of triangles that are removed. 14.The network resource controller of claim 10, wherein removing edges froma portion of the plurality of triangles includes: determining a minimumangle value of angles for each triangle; and comparing the minimum anglevalue to a predetermined value, wherein longest edges of the triangleswhose minimum angles are less than the threshold value are the edges ofthe portion of the plurality of triangles that are removed.
 15. Thenetwork resource controller of claim 10, wherein removing edges from aportion of the plurality of triangles includes: determining lengths ofthe longest edges of the triangles; determining minimum angles of thetriangles; determining ratios between respective longest edge lengthsand respective minimum angles for each triangle; and comparing theratios to a predetermined value, wherein longest edges of the triangleswhose ratios are less than the threshold value are the edges of theportion of the plurality of triangles that are removed.
 16. The networkresource controller of claim 10, wherein the operations furthercomprise: before removing the edges, identifying a plurality of triangleedges as candidates for removal, and storing triangles associated withthe candidate edges in the second memory; determining whether an edge ofa first triangle that is a candidate for removal is shared with a secondtriangle; when the edge of the first triangle is shared with the secondtriangle, determining whether the second triangle has an edge that hasbeen removed or is a candidate for removal; and when the second triangledoes not have an edge that has been removed or is a candidate forremoval, retaining the shared edge.
 17. The network resource controllerof claim 10, wherein the operations further comprise: before removingthe edges, identifying a plurality of triangle edges as candidates forremoval, and storing triangles associated with the candidate edges inthe second memory; determining whether an edge of a first triangle thatis a candidate for removal is shared with a second triangle; when theedge of the first triangle is shared with the second triangle,determining whether the second triangle has an edge that has beenremoved or is a candidate for removal; and when the second triangle hasan edge that has been removed or is a candidate for removal, removingthe shared edge from the first and second triangles.
 18. The networkresource controller of claim 17, wherein, when the edge of the firsttriangle is not shared with the second triangle, the edge is removed.